At `STP`, the order of mean square velocity of molecules of `H_(2)`, `N_(2)`, `O_(2)`, and `HBr` is

Options

A. `H_(2)ltN_(2)ltO_(2)ltHBr`
B. `HBrltO_(2)ltN_(2)ltH_(2)`
C. `H_(2)ltN_(2)=O_(2)ltHBr`
D. `HBrltO_(2)ltH_(2)ltN_(2)`

Explanation

To determine the order of mean square velocity of molecules of \( H_2 \), \( N_2 \), \( O_2 \), and \( HBr \) at STP (Standard Temperature and Pressure), we can follow these steps:

### Step 1: Understand the Formula
The root mean square velocity (\( u_{rms} \)) of a gas is given by the formula:
\[ u_{rms} = \sqrt{\frac{3RT}{M}} \]
where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molar mass (molecular weight) of the gas.

### Step 2: Identify Molar Masses
Next, we need to find the molar masses of the gases involved:
- For \( H_2 \) (Hydrogen), the molar mass \( M = 2 \, g/mol \)
- For \( N_2 \) (Nitrogen), the molar mass \( M = 28 \, g/mol \)
- For \( O_2 \) (Oxygen), the molar mass \( M = 32 \, g/mol \)
- For \( HBr \) (Hydrogen Bromide), the molar mass \( M = 1 + 80 = 81 \, g/mol \)

### Step 3: Analyze the Relationship
From the formula, we can see that the root mean square velocity is inversely proportional to the square root of the molar mass:
\[ u_{rms} \propto \frac{1}{\sqrt{M}} \]
This means that a lower molar mass will result in a higher root mean square velocity.

### Step 4: Order the Molar Masses
Now, we can order the gases based on their molar masses:
- \( H_2 \): 2 g/mol (lightest)
- \( N_2 \): 28 g/mol
- \( O_2 \): 32 g/mol
- \( HBr \): 81 g/mol (heaviest)

### Step 5: Determine the Order of Mean Square Velocity
Since \( u_{rms} \) is inversely proportional to the square root of the molar mass, the order of mean square velocity from highest to lowest will be:
1. \( H_2 \) (highest velocity)
2. \( N_2 \)
3. \( O_2 \)
4. \( HBr \) (lowest velocity)

Thus, the order of mean square velocity is:
\[ H_2 > N_2 > O_2 > HBr \]

### Conclusion
The correct answer is that the order of mean square velocity at STP is:
\[ H_2 > N_2 > O_2 > HBr \]